Asimov was a creative thinker, and a beloved science fiction author. Sad to say, he was not the best writer in the world, having no notion of character development and falling into cliche far too often. Having said that, it's possible to read Asimov's books with great enjoyment if you overlook these faux pas.
"The Naked Sun" is a continuation of "The Caves of Steel", introducing the detective pair Lije Bailey, human, and Daneel Olivaw, robot. In "Caves", the pair team up for the first time to solve the murder of a Spacer, an outworlder living on steel-clad, subterranean Earth. Based on their success, the duo are tapped to solve a murder mystery on Solaria, one of the Spacer planets, along with Aurora, that are the first extra-terrestrial settlements of human beings.
Solaria is a peculiar place. The invention of tri-dimensional television projection (which sounded futuristic when the novel was written but now sounds plausible) was adopted by the Solarians with fervor, so much so, that actual physical contact and presence is considered on par with bathroom subjects. The rich planet, with its lavish estates of orchards, factories or farms, is presided over by a limited number of Solarians who live in splendid isolation, surrounded by fleets of robots to run their enterprises. From status (only a few people and many robots) the Solarians first limited physical contact as a way of showing wealth, then it became a mania, a sort of agoraphobia, where breathing the air that is polluted by another's presence is considered more than a bit distasteful. Solarians are quite social--but all socializing is done via tridimensional projection. Only husbands and wives (and the occasional doctor) are ever tolerated up close.
So, in a world where physical proximity and of course, sexual intercourse a necessary but unpleasant evil (they hadn't considered artificial implantation?) how does a MURDER occur if an individual could not stand to be in the presence of another and all robots are guided by the Three Laws and cannot harm a person? This is the puzzle Lije and Daneel are to solve. It's complicated by the disturbing presence of Gladia, the beautiful widow of the victim. She is the prime suspect, of course, but what was her motive?
Lije is sadly, cloned from the hard-boiled detective cliche like Sergeant Friday of "Dragnet", but less so in "Naked Sun" than "Caves of Steel." Gladia, however, is quite successful as the troubled woman. The plot of this book is intricate, and the novel flies by--a page-turner. Along with "The Gods Themselves", I think this is one of Asimov's best novels.